Random Walks in Finance
Bachelier’s 1900 thesis entitled “Théorie de la Spéculation” contained both the first formulation of the theory of random walks, as well as an empirical analysis on market data.
Bachelier made several assumptions on markets, which become known as the efficient market hypothesis. He postulates that:
- Successive price movements are statistically independent
- In a perfect market, all information is accounted for by the present price
- In an efficient market, small irregularities are allowed, within the applicable transaction costs
- In a complete market, there are both buyers and sellers at any quoted price. On average, the market does not believe in a net movement.